The bang-bang property of time and norm optimal control problems for parabolic equations with time-varying fractional Laplacian
2019 ◽
Vol 25
◽
pp. 7
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Keyword(s):
In this paper, we establish the bang-bang property of time and norm optimal control problems for parabolic equations governed by time-varying fractional Laplacian, evolved in a bounded domain of ℝd. We firstly get a quantitative unique continuation at one point in time for parabolic equations governed by time-varying fractional Laplacian. Then, we establish an observability inequality from measurable sets in time for solutions of the above-mentioned equations. Finally, with the aid of the observability inequality, the bang-bang property of time and norm optimal control problems can be obtained.
2007 ◽
Vol 25
(1)
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pp. 37-48
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2005 ◽
Vol 82
(2)
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pp. 193-202
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2018 ◽
Vol 11
(6)
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pp. 1031-1060
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2020 ◽
Vol 8
(4)
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pp. 581-600